Chapter 6.3, Problem 43E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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Median Age The table shows the median ages of the U.S. resident population for the years 2005 through 2013. *(Source: U.S. Census Bureau)*

Year |
2005 | 2006 | 2007 | 2008 | 2009 | |

Median age |
36.2 | 36.3 | 36.5 | 36.7 | 36.8 | |

Year |
2010 | 2011 | 2012 | 2013 | ||

Median age |
37.2 | 37.3 | 37.5 | 37.6 |

Spreadsheet at LarsonAppliedCaIculus.com

(a) Use Simpson’s Rule to estimate the average median age over the time period.

(b) A model for the data is

*t* is the year, with

(c) Compare the results of parts (a) and (b).

**(a)**

To determine

**To calculate:** The average median age over the time period for the table that shows the median ages of the U.S. resident population for the years 2005 through 2013.

Year | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |

Median Age | 36.2 | 36.3 | 36.5 | 36.7 | 36.8 | 37.2 | 37.3 | 37.5 | 37.6 |

Explanation

**Given Information:**

The table shows that the median ages of the U.S. resident population for the years 2005 through 2013.

Year | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |

Median Age | 36.2 | 36.3 | 36.5 | 36.7 | 36.8 | 37.2 | 37.3 | 37.5 | 37.6 |

**Formula used:**

Simpson’s Rule:

If *f* is continuous on *n* is an even integer, then

The average median can be find as,

**Calculation:**

Since, the given table shows the population from 2005 to 2013.

So, here

Now, use the table and substitute

**(b)**

To determine

**To calculate:** The average median age over the time period for the model of data

**(c)**

To determine

The comparison between the results obtained from the average median age by using table of data and the average median age over the time period using model of the data.

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